In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles which are emitted. If the end nucleus is $${}_Z^A$$X, A and Z are given by :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $$\mu $$F. All values in the circuit are in $$\mu $$F.